the painting on the wall is too small and too high. Are those lights on either side?

Yes, two lights.

What colour would you paint the wall?

I don't mind the wall color, but if really wanting to change, I would go lighter in a shade close to existing sofa.. I agree the picture needs to be lower. The TV, fireplace, and built ins bother me. I would consider hiring a carpenter to do some trim work around all of it to make it all appear as a single built in unit and give height and some flare to fireplace.

I would lower your picture to around 8" above your sofa. I think adding some color in your pillows and perhaps a throw or two would be a good place to start. Maybe a woven shade or some kind of blind on your window instead of the off-white curtain? Aa. Area rug would add to the "cozy factor".

I think the TV would look better if it were lower. That would involve filling in the top shelves so I understand why you might not want to go that route. As mentioned above - beefing up the shelves and trim would help. I might be inclined to fill the shelves or at least the bottom couple with matching baskets to add some texture and storage. Place one or two larger items on the remaining shelves instead of many smaller ones.

I agree that the picture needs to be lowered significantly. I would lose the sconces or replace with something much more substantial. Also agree that you could really improve the impact of the fireplace wall with wood trim and it should not be very expensive. I would then tidy up the shelves and use them more for display than function. I might move the picture to the other wall and replace the picture with a substantial mirror. The reeds by the window are on the right path but need to have a much taller container with again much taller reeds or branches. Agree with layering the furniture with throw, pillows, etc to add interest. Add either a small round coffee table (dark wood) or a round ottoman with a tray on top. Accessorize the table or tray but don't go overboard, a few items only. But, the biggest improvement I would make is the window coverings. I would add panels from floor to ceiling. I believe that will make the statement that the room is currently missing.

Wainscoating or Crownmoulding to bring the eye level down.

I think you need taller drapery! I don't like the way the top of the rod and tv are on the same level. You could still have functional drapery on a traversing rod..that is the only way to open and close them when the curtains are that tall. I would find a coordinating pattern to the drapery panels and throw them onto the couch. The picture needs to be down between the lights on the wall with the top of the picture just a few inches higher than the lights. Moldings would be a great addition but the wainscoating is too traditional for your transitional style. I don't know how they will pull off making the fireplace and the shelving unit to look great as one piece but I think it's worth getting someone out to see what magic they can work out!

Here is an idea.